Preheat the oven to 170C/340F/Gas 3½
Wrap the whole garlic bulb in aluminium foil and place on a tray in the oven. Roast for 40-45 minutes, or until soft.
When the garlic is cool enough to handle, cut the top off of the bulb. Squeeze out all the garlic and finely chop.
Pour the double cream into the bowl of a freestanding mixer and beat for 3-5 minutes, or until the mixture turns to solid fatty lumps with a liquid base.
Line a colander with a clean muslin cloth and place it over a bowl. Tip the mixture into the colander and wrap the muslin tightly around the cream. Squeeze out all the liquid so that you have a solid mass of butter in the muslin, then discard the liquid.
Tip the butter into the bowl, add the chopped garlic and a generous pinch of salt. Stir in a third of the chopped basil and mix once more.
Heat a large frying pan or sauté pan until hot, add all but two tablespoons of the extra virgin olive oil and the shallot and gently fry for a minute.
Add the tinned tomatoes and the rest of the basil, reserving two sprigs for garnish, then simmer for 2-3 minutes.
While the soup simmers, heat a griddle pan until very hot and char the bread on both sides, then slather with the garlic butter and place in the oven to warm through.
Blend the soup using a stick blender or a food processor until you have a fine pureé. Season, to taste, with salt and black pepper.
Serve the soup in bowls with the reserved olive oil drizzled over the top and a scattering of basil leaves, and the garlic bread alongside.